Liverpool climbed to the top of the Premier League as Darwin Nunez ended his goal drought to inspire a 2-0 win against Burnley, while Chris Wood's hat-trick against his old club Newcastle gave Nuno Espirito Santo his first victory as Nottingham Forest boss on Tuesday.

Jurgen Klopp's side took an early lead through Nunez at Turf Moor and held on despite wasting a host of chances.

Nunez's eighth goal this season was his first for 12 games since he netted against Bournemouth in the League Cup on November 1.

Diogo Jota, back from a month's injury absence, wrapped up the victory late on to leave Liverpool two points above second placed Arsenal, who have a game in hand.

Third placed Aston Villa would move level on points with Liverpool, behind them on goal difference, if they beat Manchester United later on Tuesday.

Arsenal can regain top spot with a victory at home to West Ham on Thursday.

After successive draws with Manchester United and Arsenal prior to Christmas, this was an essential victory for Liverpool's title ambitions.

Wood left Newcastle to join Forest in a £15 million ($19 million) deal in June, but had scored only four times for his new club.

The 32-year-old New Zealand international managed just two league goals for Newcastle last term, but he surpassed that meagre total with a treble in 60 minutes at St James' Park.

Alexander Isak's first half penalty put Newcastle ahead, but Wood equalised just before the break.

He struck twice more in the second half to hand former Tottenham manager Nuno his maiden victory with Forest in his second game in charge after replacing the sacked Steve Cooper.

Racism row

It was Forest's first win in eight games and only their second success in their last 15 matches.

Forest moved five points clear of the relegation zone ahead of the rest of the day's matches.

Nuno's first game in charge ended in a painful 3-2 stoppage-time defeat against Bournemouth at the City Ground last weekend.

Newcastle's fifth defeat in their last seven games in all competitions leaves them seven points adrift of the top four in seventh place.

Luton boss Rob Edwards said South Yorkshire Police are investigating an alleged racist comment towards Carlton Morris in his side's 3-2 win at fellow strugglers Sheffield United.

Morris complained of a comment made from a United fan late in the second half, which left him "pretty angry", and the police have spoken to him.

It soured what was a great day for Morris as he came off the bench to create two own goals in four minutes as third bottom Luton came from 2-1 down to beat the division's bottom club.

"There was an alleged racist comment, the police are dealing with that, they have spoken to Carlton and got his take on it, so it is with them now," Edwards said.

Fulham boss Marco Silva insisted his goalkeeper Bernd Leno "touched" but "didn't push" a ball boy during the Cottagers' 3-0 defeat at Bournemouth.

The second-half incident occurred when Leno went to collect the ball from the youngster's outstretched hand before using his own hand to make deliberate contact with the shoulder of the boy, who appeared to take a step back for balance.

The 31-year-old German later returned to apologise to the ball boy for the encounter, though Silva was adamant the interaction had been exaggerated.

"Have you seen him pushing? I didn't see this. Yes, he apologised. I spoke with Bernd about it," Silva said.